Timeline for The probability that a random number N has at least M factors
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2012 at 22:17 | vote | accept | mndc | ||
| Sep 20, 2012 at 0:51 | history | edited | Kaveh |
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| Sep 3, 2012 at 8:06 | answer | added | Brad Rodgers | timeline score: 3 | |
| Sep 2, 2012 at 18:00 | comment | added | Anthony Quas | I'd recommend looking at the beautiful and accessible MAA book by Mark Kac, Statistical Independence in Probability, Analysis and Number Theory. This deals in a very nice way with the number of divisors function. | |
| Sep 2, 2012 at 15:52 | answer | added | user9072 | timeline score: 4 | |
| Sep 2, 2012 at 13:31 | answer | added | Igor Rivin | timeline score: 2 | |
| Sep 2, 2012 at 11:54 | comment | added | LeBlanc | @Stefan I think the questioner is trying to ask something like: "Given positive integer $N$, and numbers $L,M< N$, if you pick a random number in the set $\{N+i,N−i|0\leq i<L \}$ (Numbers "around" $N$) , what is the probability that it has at least $M$ factors? "Or maybe not so symmetric sample around $N$. What if we pick a number out of the set of all numbers with the same number of digits as $N$ instead? | |
| Sep 2, 2012 at 11:05 | comment | added | Stefan Geschke | Also, in what sense is the probability of $N$ being prime $1/\ln(N)$? Given $N$, the probability that $N$ is prime is either $0$ or $1$. | |
| Sep 2, 2012 at 11:01 | comment | added | Charles Matthews | Try en.wikipedia.org/wiki/Divisor_function for the basics on the function d(n). | |
| Sep 2, 2012 at 11:01 | comment | added | Stefan Geschke | You are clearly talking about infinitely many $N$ here. What is the distribution on this infinite set of numbers? Or do you want to know the limit of the probablities of $N$ having at least $M$ factors for $N$ in an interval $(a,b)$ where $a$ is large compared to $M$ and $b$ goes to infinity? In this case you would have to argue why this limit exists. | |
| Sep 2, 2012 at 10:37 | history | asked | mndc | CC BY-SA 3.0 |